Over at your local high school, the main hallway has a bank of 100 lockers.
All of these lockers, labeled 1 through 100, start with their doors closed.
The resident class clown decides to open every locker door.
He then returns to the front of the row and
toggles (opens/closes) every 2nd locker door (2,4,6,8...) in the hallway.
That is, he goes to every 2nd locker, if it's open, he closes it,
if it's closed, he opens it.
The class clown repeats this for every 3rd locker (3,6,9...),
then every 4th locker (4,8,12...), then every 5th (5,10,15...), etc.
until he finally repeats for every 100th locker.
After the class clown is done, which locker numbers will end up closed,
which will end up open?